Backtracking-1 Complete

CombinationSum.java

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+/*
+* Approach1: The problem is similar to coin change. So go exhaustive and explore all options
+- The idea is to do a 0/1 recursion -> choose/not choose
+- TC: O(2^m+n) -> two input variables, candidates of length n and target
+- SC: O(n) -> path array
+ */
+class Solution {
+    List<List<Integer>> res;
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        this.res = new ArrayList<>();
+        List<Integer> path = new ArrayList<>();
+        helper(candidates, 0, path, target);
+        return res;
+    }
+
+    private void helper(int[] candidates, int idx, List<Integer> path, int target){
+        //base
+        // if we have selected more candidates then required or idx goes out of bound
+        if(target < 0 || idx >= candidates.length)
+            return;
+
+        //once we have a combination that is equal to the target, add that to the result
+        if(target == 0){
+            //create a deep copy of the path before adding it to the result as we are using the same reference of the path
+            res.add(new ArrayList<>(path));
+            return;
+        }
+
+        //logic
+
+        //0-> not choose
+        helper(candidates, idx + 1, path, target);
+        //1-> choose
+
+        //add element in the path
+
+        //action
+        path.add(candidates[idx]);
+        //recurse
+        helper(candidates, idx, path, target - candidates[idx]);
+        //backtrack
+        path.remove(path.size() - 1);
+    }
+}

Subsets.java

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+/*
+* Approach: 
+ - The idea is to use 0/1 recursion to explore all subsets of the array
+ - Once we have reached the end, add it to the result
+ -TC: O(2^n * n)-> n for copying the path to the resultant array * choose/not choose for n elements so 2^n
+ - SC: O(n) -> recursion stack space
+ */
+class Solution {
+    List<List<Integer>> res;
+    public List<List<Integer>> subsets(int[] nums) {
+        this.res = new ArrayList<>();
+        List<Integer> path = new ArrayList<>();
+        helper(nums, path, 0);
+        return res;
+    }
+
+    private void helper(int[] nums, List<Integer> path, int idx){
+        //base
+        if(idx == nums.length){
+            res.add(new ArrayList<>(path));
+            return;
+        }
+        //logic
+
+        //not choose
+        helper(nums, path, idx + 1);
+         //choose 
+         //action
+         path.add(nums[idx]);
+
+         //recurse
+         helper(nums, path, idx + 1);
+         //backtrack
+         path.remove(path.size() - 1);
+    }
+}